Chapter 2.2, Problem 16PP

Interpretation Introduction

(a)

Interpretation:

The area of the rectangle needs to be calculated in the scientific notation.

Concept introduction:

The form of expressing too big or too small numbers into a convenient decimal form is known as scientific notation. Area is a quantity expressing the extent of a two-dimensional shape or a plane. Density is defined as the amount of mass per unit volume.

Answer to Problem 16PP

The area of the rectangle with sides $3\times {10}^{1}cm$ and $3\times {10}^{-2}cm$ is $9\times {10}^{-1}c{m}^2$

Explanation of Solution

Scientific notation is used to express any number as a number between 1 and 10 that is known as coefficient and is multiplied by 10 raised to a power that is known as exponent.

The area of a rectangle with sides $3\times {10}^{1}cm$ and $3\times {10}^{-2}cm$

Since Area $A=l\times b$

Therefore, $3\times {10}^{1}cm\times 3\times {10}^{-2}cm=(3\times 3)\times {10}^{1+(-2)}=9\times {10}^{-1}c{m}^2$

(b)

Interpretation Introduction

Interpretation:

The area of the rectangle of given dimensions needs to be calculated in the scientific notation.

Concept introduction:

The form of expressing too big or too small numbers into a convenient decimal form is known as scientific notation. Area is a quantity expressing the extent of a two-dimensional shape or a plane. Density is defined as the amount of mass per unit volume.

Answer to Problem 16PP

The area of a rectangle with sides $1\times {10}^{3}cm$ and $5\times {10}^{-1}cm$ is $5\times {10}^{2}c{m}^2$.

Explanation of Solution

Scientific notation is used to express any number as a number between 1 and 10 that is known as coefficient and is multiplied by 10 raised to a power that is known as exponent.

The area of a rectangle with sides $1\times {10}^{3}cm$ and $5\times {10}^{-1}cm$ :

Since Area $A=l\times b$

Therefore, $(1\times {10}^{3}cm)\times (5\times {10}^1)cm=(1\times 5)\times {10}^{3+(-1)}=5\times {10}^{2}c{m}^2$

(c)

Interpretation Introduction

Interpretation:

The density of substance needs to be calculated in the scientific notation.

Concept introduction:

The form of expressing too big or too small numbers into a convenient decimal form is known as scientific notation. Area is a quantity expressing the extent of a two-dimensional shape or a plane. Density is defined as the amount of mass per unit volume.

Answer to Problem 16PP

The density of a substance having a mass of $9\times {10}^{5}g$ and volume of $3\times {10}^{-1}c{m}^3$ is $3\times {10}^{6}g/c{m}^3$.

Explanation of Solution

Scientific notation is used to express any number as a number between 1 and 10 that is known as coefficient and is multiplied by 10 raised to a power that is known as exponent.

The density of a substance having a mass of $9\times {10}^{5}g$ and volume of $3\times {10}^{-1}c{m}^3$ :

Since Area $density=\frac{mass}{volume}$

Therefore, $density=\frac{9\times {10}^{5}g}{3\times {10}^{-1}c{m}^3}=\frac{9}{3}\times {10}^{5-(-1)}=3\times {10}^{6}g/c{m}^3$

(d)

Interpretation Introduction

Interpretation:

The density of substance of given mass and volume needs to be calculated in the scientific notation.

Concept introduction:

The form of expressing too big or too small numbers into a convenient decimal form is known as scientific notation. Area is a quantity expressing the extent of a two-dimensional shape or a plane. Density is defined as the amount of mass per unit volume.

Answer to Problem 16PP

The density of a substance having a mass of $4\times {10}^{-3}g$ and volume of $2\times {10}^{-2}c{m}^3$ is $2\times {10}^{-1}g/c{m}^3$.

Explanation of Solution

Scientific notation is used to express any number as a number between 1 and 10 that is known as coefficient and is multiplied by 10 raised to a power that is known as exponent.

The density of a substance having a mass of $4\times {10}^{-3}g$ and volume of $2\times {10}^{-2}c{m}^3$ :

Since Area $density=\frac{mass}{volume}$

Therefore, $density=\frac{4\times {10}^{-3}g}{2\times {10}^{-2}c{m}^3}=\frac{4}{2}\times {10}^{-3-(-2)}=2\times {10}^{-1}g/c{m}^3$